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J. Casademunt

Publications and source records attributed to J. Casademunt.

At least 19 recordsLinked to original sources
arXiv2017

Hydrodynamic instabilities, waves and turbulence in spreading epithelia

We present a hydrodynamic model of spreading epithelial monolayers as polar viscous fluids, with active contractility and traction on the substrate. The combination of both active forces generate an instability that leads to nonlinear traveling waves, which propagate in the direction of polarity with characteristic time scales that depend on contact forces. We show that a viscous fluid model explains a variety of observations on the slow dynamics of epithelial monolayers, in particular those that had been interpreted before as signatures of elasticity. The non-elastic nature of the waves can be tested on the basis of simple predictions of the model. Our theoretical framework provides new insights such as the interpretation of plithotaxis as a result of a strong flow-polarity coupling, and the quantification of collective force-transmission of cells in terms of the non-locality of interactions. In addition, we study the nonlinear regime of those waves deriving an exact map of the model into the Complex Ginzburg-Landau equation, which provides a complete classification of possible nonlinear scenarios. In particular, we predict the transition to different forms of weak turbulence, which in turn could explain the very unstable and irregular dynamics often observed in epithelia.

cond-mat.soft↗
arXiv2005

Collective dynamics of molecular motors pulling on fluid membranes

The collective dynamics of $N$ weakly coupled processive molecular motors are considered theoretically. We show, using a discrete lattice model, that the velocity-force curves strongly depend on the effective dynamic interactions between motors and differ significantly from a simple mean field prediction. They become essentially independent of $N$ if it is large enough. For strongly biased motors such as kinesin this occurs if $N\gtrsim 5$. The study of a two-state model shows that the existence of internal states can induce effective interactions.

q-bio.SC↗
arXiv2004

Spontaneous pinch-off in rotating Hele-Shaw flows

The dynamics of the interface between two immiscible fluids in a rotating Hele-Shaw cell are studied experimentally, theoretically and by phase-field simulations of the H-S equations. As the central, denser fluid is centrifuged, it forms fingering patterns with long, thin radial filaments ended by a droplet, alternating with incoming fingers of the outer fluid. Simulations show the length (width) of the filaments to grow (decay) roughly exponentially, and the incoming finger tips to asymptotically approach a finite radius for n-fold symmetric initial conditions; these thus tend to a stationary-shape, which is calculated. The filament width decays with a time constant which depends only on the viscosity contrast, whereas its length exhibits a completely universal growth rate, related to the run away of an isolated droplet, for which we give an exact solution. The exponential behavior is clear for high, but not low viscosity contrasts A. Both experiments and simulations show systematic pinch-off of the droplets at the tips of the filaments for low and not for high A. A lubrication approximation is derived and successfully accounts for the filament thinning; it explains why pure exponential thinning is not observed for low A, and it could clarify the presence or absence of finite-time pinch-off, since the (morphological) agreement of experiments and simulations suggests that this phenomenon is contained in the Hele-Shaw equations. For low A, the experimental time constant appears to be different from that predicted by standard Hele-Shaw boundary conditions and observed in simulations. An effective slip condition for the Poiseuille flow of inner liquid across the cell gap in the case of two liquids gives a possible explanation of this discrepancy.

physics.flu-dyn↗
arXiv2003

Phase-field models in interfacial pattern formation out of equilibrium

The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate the fronts. These fields interpolate between different constant values in each bulk phase through diffuse interfaces of finite thickness. In solidification, the phase fields can be understood as order parameters, and the model is often derived to dynamically minimise a free energy functional. However, this is not a necessary requirement, and both derivations involving a free energy (basic solidification model) and not (first viscous fingering model) are worked out. In any case, the model is required to reproduce the original free boundary problem in the limit of vanishing interface thickness. This limit and its higher order corrections, important to make quantitative contact between simulations and experiments, are discussed for both examples. Applications to fluctuations in solidification, the growth of liquid crystal mesophases, and viscous fingering in Hele-Shaw cells are presented.

cond-mat.mtrl-sci↗
arXiv2003

Intrinsic noise-induced phase transitions: beyond the noise interpretation

We discuss intrinsic noise effects in stochastic multiplicative-noise partial differential equations, which are qualitatively independent of the noise interpretation (Ito vs. Stratonovich), in particular in the context of noise-induced ordering phase transitions. We study a model which, contrary to all cases known so far, exhibits such ordering transitions when the noise is interpreted not only according to Stratonovich, but also to Ito. The main feature of this model is the absence of a linear instability at the transition point. The dynamical properties of the resulting noise-induced growth processes are studied and compared in the two interpretations and with a reference Ginzburg-Landau type model. A detailed discussion of new numerical algorithms used in both interpretations is also presented.

cond-mat.stat-mech↗
arXiv2003

Dynamics of Turing patterns under spatio-temporal forcing

We study, both theoretically and experimentally, the dynamical response of Turing patterns to a spatio-temporal forcing in the form of a travelling wave modulation of a control parameter. We show that from strictly spatial resonance, it is possible to induce new, generic dynamical behaviors, including temporally-modulated travelling waves and localized travelling soliton-like solutions. The latter make contact with the soliton solutions of P. Coullet Phys. Rev. Lett. {\bf 56}, 724 (1986) and provide a general framework which includes them. The stability diagram for the different propagating modes in the Lengyel-Epstein model is determined numerically. Direct observations of the predicted solutions in experiments carried out with light modulations in the photosensitive CDIMA reaction are also reported.

physics.chem-ph↗
arXiv2002

Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, non-conserved and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which scale with capillary number as ell_1 ~ b_0(c Ca)^{-1/2} and ell_2 ~ b_0 Ca^{-1}. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments.

cond-mat.stat-mech↗
arXiv2002

Periodic forcing in viscous fingering of a nematic liquid crystal

We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). We observe undulations at the sides of the fingers which correlate with the switching frequency and with tip oscillations which give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise-induced) side branching. We conclude that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.

cond-mat.soft↗
arXiv2002

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.

nlin.PS↗
arXiv2002

Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated to the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-KPZ universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations, kinetic roughening, and the noise-induced pushed-pulled transition, which is predicted and observed for the first time. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

cond-mat.stat-mech↗
arXiv2001

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.

nlin.PS↗
arXiv2001

Sidebranching induced by external noise in solutal dendritic growth

We have studied sidebranching induced by fluctuations in dendritic growth. The amplitude of sidebranching induced by internal (equilibrium) concentration fluctuations in the case of solidification with solutal diffusion is computed. This amplitude turns out to be significantly smaller than values reported in previous experiments.The effects of other possible sources of fluctuations (of an external origin)are examined by introducing non-conserved noise in a phase-field model. This reproduces the characteristics of sidebranching found in experiments. Results also show that sidebranching induced by external noise is qualitatively similar to that of internal noise, and it is only distinguished by its amplitude.

nlin.PS↗
arXiv2000

Systematic weakly nonlinear analysis of interfacial instabilities in Hele-Shaw flows

We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general. It includes both the channel geometry driven by gravity and pressure, and the radial geometry with arbitrary injection and centrifugal driving. We find the finite radius of convergence of the mode-coupling expansion. In the channel geometry we carry out the calculation up to third-order couplings, which is necessary to account for the time-dependent Saffman-Taylor finger solution and the case of zero viscosity contrast. Both in the channel and the radial geometries, the explicit results provide relevant analytical information about the role that the viscosity contrast and the surface tension play in the dynamics. We finally check the quantitative validity of different orders of approximation against a physically relevant, exact time-dependent solution. The agreement between the low order approximations and the exact solution is excellent within the radius of convergence, and reasonably good even beyond that.

nlin.PS↗
arXiv1999

Viscous fingering in liquid crystals: Anisotropy and morphological transitions

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip-splitting and side-branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature and applied pressure are varied. Our observations are also consistent with previous experimental evidence in viscous fingering within an etched cell and simulations of solidification.

cond-mat.soft↗
arXiv1999

Interface dynamics in Hele-Shaw flows with centrifugal forces. Preventing cusp singularities with rotation

A class of exact solutions of Hele-Shaw flows without surface tension in a rotating cell is reported. We show that the interplay between injection and rotation modifies drastically the scenario of formation of finite-time cusp singularities. For a subclass of solutions, we show that, for any given initial condition, there exists a critical rotation rate above which cusp formation is prevented. We also find an exact sufficient condition to avoid cusps simultaneously for all initial conditions. This condition admits a simple interpretation related to the linear stability problem.

cond-mat↗
arXiv1999

Two-finger selection theory in the Saffman-Taylor problem

We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \it unequal \rm fingers advancing with the same velocity but with different relative widths $λ_1$ and $λ_2$ and different tip positions. For vanishingly small dimensionless surface tension $d_0$, an infinite discrete set of values of the total filling fraction $λ= λ_1 + λ_2$ and of the relative individual finger width $p=λ_1/λ_2$ are selected out of a two-parameter continuous degeneracy. They scale as $λ-1/2 \sim d_0^{2/3}$ and $|p-1/2| \sim d_0^{1/3}$. The selected values of $λ$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given.

cond-mat.stat-mech↗
arXiv1999

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. I. Theoretical approach

We present a phase-field model for the dynamics of the interface between two inmiscible fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. With asymptotic matching techniques we check the model to yield the right Hele-Shaw equations in the sharp-interface limit and compute the corrections to these equations to first order in the interface thickness. We also compute the effect of such corrections on the linear dispersion relation of the planar interface. We discuss in detail the conditions on the interface thickness to control the accuracy and convergence of the phase-field model to the limiting Hele-Shaw dynamics. In particular, the convergence appears to be slower for high viscosity contrasts.

cond-mat.soft↗